Higher fuel consumption standards are driving the progress and applications of automotive light-weight materials. Among them, fiber-reinforced thermoplastic (FRT) composites are favored due to excellent strength/weight properties. It is important to understand the fiber reinforcement microstructure.
FIG. 1 shows an FRT composite article with a fan-gated plaque geometry having a marked region C at the center, and FIG. 2 shows a well-known skin-shell-core structure found in an experimental flow-direction orientation component across the thickness of the molded FRT article along the thickness direction at the region C shown in FIG. 1. One of the important orientation descriptors is the flow direction orientation component (A11) corresponding to the flow direction, referring to the degree of orientation of fibers along the flow direction. In general, a high value of the flow direction orientation component (A11) would indicate a great deal of fibers laying in the flow direction
Those fibers found in the shell region (near the cavity wall with high shear rates) are strongly aligned in the flow direction, but the other fibers in the core region (near the cavity center with low shear rates) are transverse to the flow direction. The skin region indicates a decrease of fiber alignment since the fibers at the front is influenced by fountain flow and rapidly frozen close to the cold mold. In order to manufacture safer FRT products with higher strength, a trend to use higher fiber concentration or longer fiber length is recently attempted in automotive, aerospace and energy industries. In particular, a great core-width feature is found in such a condition. Unfortunately, the conventional fiber orientation simulation technique cannot predict such core width, because it predicts a much thinner core region as compared to the experimental orientation data.
To solve this shortage, Huynh proposed one possible mechanism in his master's thesis (Huynh H M. Improved fiber orientation predictions for injection molded composites. Master's Thesis, University of Illinois at Urbana-Champaign; 2001). In Huynh's work, a Yield-WLF-Cross viscosity model was produced by combining the standard WLF-Cross model and the Papanastasiou model (Papanastasiou T C. Flows of materials with yield. J Rheol 1987; 31:385). Furthermore, the Yield-WLF-Cross viscosity model was then implemented into an ORIENT program to predict the fiber orientation, wherein the ORIENT program uses a finite difference scheme based on the Hele-Shaw approximation and the Folgar-Tucker orientation equation (Bay R S, Tucker III C L. Fiber orientation in simple injection moldings. Part i: Theory and numerical methods. Polymer Composites 1992; 13:317-331 and Bay R S, Tucker III C L. Fiber orientation in simple injection moldings. Part ii: Experimental results. Polymer Composites 1992; 13:332).
FIG. 3 shows viscosity versus shear rate for WLF-Cross and Yield-WLF-Cross viscosity models according to the prior art (disclosed in Huynh's work). It appears that the Yield-WLF-Cross model involves two regions: the low-shear-rate yield stress region and the high-shear-rate shear thinning region, without an obvious Newtonian plateau, differing from the standard WLF-Cross model. In addition, the yield-stress viscosity at two different temperatures is the same; namely, the temperature-independent yield-stress viscosity is constant. However, in the real world, the yield-stress viscosity is different at different temperatures; in other words, the Huynh's work does not match the experimental data.
FIG. 4 shows the predicted flow direction orientation component (A11) with respect to the normalized thickness (z/h), using different viscosity models according to the prior art (disclosed in Huynh's work). The standard WLF-Cross viscosity model predicts a very narrow core as compared with the experimental data. The core region is widened by applying the Yield-WLF-Cross viscosity model; however, Huynh's work shows a flat orientation plateau/well over a core region, which does not match the experimental data. In conclusion, a yield stress does not provide adequate improvement to the orientation predictions.
In particular, over the last three decades, great effort has been made to describe the flow-induced variation of fiber orientation in fiber suspension rheology. The injection molding software has adopted several theoretical approaches, including the Folgar-Tucker IRD (Isotropic Rotary Diffusion) model, the Phelps-Tucker ARD (Anisotropic Rotary Diffusion) model, and the Wang-Tucker RSC (Reduced Strain Closure) model (Wang J. Improved fiber orientation predictions for injection molded composites. Ph.D. Thesis, University of Illinois at Urbana-Champaign; 2007 and Phelps J H. Processing-microstructure models for short-fiber and long-fiber thermoplastic composites. Ph.D. Thesis, University of Illinois at Urbana-Champaign; 2009). Recently, Tseng et al. developed a fiber orientation model called the iARD-RPR model (Improved Anisotropic Rotary Diffusion model combined with Retarding Principal Rate model, Tseng H-C, Chang R-Y, Hsu C-H. Method and computer readable media for determining orientation of fibers in a fluid. U.S. Pat. No. 8,571,828; 2013 and Tseng H-C, Chang R-Y, Hsu C-H. Phenomenological improvements to predictive models of fiber orientation in concentrated suspensions. J Rheol 2013; 57:1597-1631).
However, using these conventional models, the predicted fiber core width is too narrow or not broad enough, as shown in FIG. 2. So far, the underlying cause of the inaccurate prediction of the core width is not clear to the orientation prediction area. More importantly, the anisotropic orientation prediction strongly influences the warpage and structure analyses of a final molded FRT article.
This “Discussion of the Background” section is provided for background information only. The statements in this “Discussion of the Background” are not an admission that the subject matter disclosed in this “Discussion of the Background” section constitutes prior art to the present disclosure, and no part of this “Discussion of the Background” section may be used as an admission that any part of this application, including this “Discussion of the Background” section, constitutes prior art to the present disclosure.